Yes this makes sense.
I don't know about automating the process, but leveling the individual areas for printing can be done quickly using the straighten feature of the Ruler Tool.
I would just use a solid rectangles created with the Rectangle Tool. Reduce it's opacity so you can visualize your positioning and overlapping. Use the Cmd/Cntrl + J command to duplicate as many times as needed.
Use Free Transform to move and position the rectangles. Be sure to name each area layer to keep track.
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Then select the map layer.
Cmd/Cntrl + click the layer of the area you would like to copy.........this makes a selection of the rectangle.
Then hit Cmd/Cntrl + J to copy that selection to it's layer. Again, be sure to name the areas to keep track.
Once you have all the areas copied to their own layers......
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......use the Ruler Tool to straighten and the Move Tool to position.
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Now create a new document the exact size of your rectangle, copy & paste or drag and drop.
( You can also make a selection of area (1,2,3, leveled) copy, new doc, paste)
Ready to be printed.
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